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Australian Intermediate Mathematics Olympiad 2015 Question 8

AIMO AUSTRALIA · Australian Intermediate Mathematics Olympiad 2015

Question 8

Determine the number of non-negative integers $x$ that satisfy the equation $\left\lfloor\frac{x}{44}\right\rfloor=\left\lfloor\frac{x}{45}\right\rfloor$. (Note: if $r$ is any real number, then $\lfloor r\rfloor$ denotes the largest integer less than or equal to $r$.)

Numerical answer only; a non-negative integer less than 1000.